Frank Sinatra Jr, who has died aged 72, did not make things easy for himself when he decided to forge a career as a singer, performing in the style of the most famous entertainer of the 20th century, who happened to be his father. Although the name opened many doors, the comparison could never be in his favour.

Not surprisingly, he lacked distinctiveness. Without the name, he would have been just another of the thousands of crooners trying to recreate the mood of Songs for Swingin’ Lovers. The times had changed, too, and younger entertainers were expected to move with them. Favouring the sort of Broadway songs associated with his father, he found himself, in his own words, “trying to sell antiques in a modern appliance store”.

Frank Sinatra Jr dies unexpectedly on singing tour

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Famous from birth as the second of the three children – and the only son – fathered by Frank Sinatra with his first wife, the former Nancy Barbato, Frank Jr made his greatest impact on the public consciousness in 1963, when he was kidnapped by a gang of three men and ransomed for almost a quarter of a million dollars. His father was then at the peak of his fame, a confidant of presidents and holding court with the Rat Pack in Las Vegas, and the affair made headlines around the world.

Frank Sinatra Jr in 1948 with his father, Frank, and sister Nancy. Nancy also became a singer. Photograph: Snap/Rex/Shutterstock

The young man recovered from the ordeal and persevered with his musical career, first touring with the band carrying the name of the Tommy Dorsey, his father’s former employer, directed after the trombonist’s death in 1956 by Sam Donahue, and then going on to record several albums. Later he acted as his father’s musical director. After Frank Sr’s death he picked up the microphone again, albeit unenthusiastic about his show being billed, as it often was, “Sinatra Sings Sinatra”.

Born in Jersey City while his 29-year-old father, still in the flush of his early fame, was away in the Hollywood studios, he was named after Franklin Delano Roosevelt, a man greatly admired in the Sinatra household. This was a time when fans would camp outside the home in Hasbrouck Heights, New Jersey; that spring the family moved to California, first to a house inside walled grounds in the San Fernando Valley that had formerly belonged to Nancy Astor.

The child was known to the family as “Frankie”. His features were familiar, but they lacked the compelling gauntness or the special light in the eyes that had transfixed a generation of bobbysoxers. They became increasingly unfamiliar to his father, who was spending large amounts of time away and eventually, after flings with Lana Turner, Marilyn Monroe and others, embarked on a serious relationship with Ava Gardner, who would become the second of his four wives. Although always well provided for, and the recipients of paternal visits at Christmas, the Fourth of July and birthdays, the family grew up aware of him, like the rest of the world, largely through the sound of his voice on national radio.

Frank Sinatra Jr performing with the Tommy Dorsey Orchestra at the Flamingo hotel in Las Vegas, 1963. Photograph: John Cook/EPA

At 19, Frank Jr joined the Dorsey band. On 8 December 1963, 16 days after the assassination of President John F Kennedy, for whom his father had campaigned, he was appearing at Harrah’s Club in Lake Tahoe when he was abducted at gunpoint. The attorney general, Bobby Kennedy, and the head of the FBI, J Edgar Hoover, were enlisted in the search. Three days later the ransom – $240,000 in used small bills, provided by his father – was deposited by an FBI man at a designated drop-off point, and Frank Jr, who had been held in a house in the Los Angeles suburb of Canoga Park, was bundled out of a car on the San Diego Freeway and left to walk to safety. The newly widowed Jackie Kennedy found time to write his father a letter saying how happy she was to hear of the release.

In March 1964, three men – John Irwin, a house painter, Barry Keenan, an unemployed salesman, and Joseph Amsler, an unemployed shellfish diver – were convicted of the kidnapping and sentenced to prison terms. For many years afterwards Frank Jr had to put up with rumours that the whole business had been arranged in order to generate publicity for his father.

He resumed his career, which continued on its quiet way until the late 1980s, when he joined his father on the road, maintaining a discreet presence as the spotlights played on the ageing star, in whose delivery and demeanour the first signs of dementia would soon be apparent. In the years after his father’s death in 1998, Frank Jr appeared as himself in episodes of Family Guy and The Sopranos, where he was mockingly referred to as “chairboy of the board” by a fellow player in Tony Soprano’s high-stakes poker game. Last September, as part of the celebrations of his late father’s centenary, he sang the national anthem at Dodger Stadium, Los Angeles.

His 1998 marriage to Cynthia McMurrey ended in divorce two years later. He is survived by his son, Michael, from a previous relationship; by his mother; and by his sisters, Nancy and Tina.